Implicit Integration and Consistent Tangent Stiffness of Cyclic Plastic Constitutive Models Based on a General Form of Strain Hardening and Dynamic Recovery. 1st Report. Formulation.

Abstract

This paper describes fully implicit integration and consistent tangent stiffness of rate-independent cyclic plastic constitutive models in which a general form of strain hardening and dynamic recovery is employed to represent the multilinear, as well as nonlinear, evolution of back stress. First, using the backward Euler discretization and the return mapping algorithm, a nonlinear scalar equation is derived to determine the increment of plastic strain induced by a prescribed strain increment in initially isotropic materials. A successive substitution method is suggested to solve the nonlinear equation and to complete the implicit integration. Then, the discretized constitutive relations are differentiated to derive a consistent tangent modulus, in which the generality of strain hardening and dynamic recovery is retained for the evolution of back stress. Finally, the constitutive parameters introduced in deriving the nonlinear scalar equation and the consistent tangent modulus are specified for three nonlinear kinematic hardening rules, which have different forms of dynamic recovery, leading to their distinctive capabilities of simulating ratchetting and cyclic stress relaxation.